Volume entropy, systole and stable norm on graphs
Florent Balacheff
Abstract
We study some new isoperimetric inequalities on graphs. We etablish a relation between the volume entropy (or asymptotic volume), the systole and the first Betti number of weighted graphs. We also find bounds for the volume, associated to some special measure, of the unit ball for the stable norm of graphs.
Create a lesson
Related papers
The Bézout inequality for mixed volumes characterizes simplices
Dylan Langharst, Shouda Wang
Affine dual Minkowski problem for general measures
Cheng Zhang, Hailin Jin
Algebraically independent distances and rigid metrics
Yoshito Ishiki
On the Geometry of Wasserstein Barycenter II: Riemannian Rigidity, Essential Non-Branching, and Finsler Models
Bang-Xian Han, Deng-Yu Liu
A Weak Topology on Metric Spaces
Armando W. Gutiérrez, Olavi Nevanlinna
Uncentered Blaschke-Santaló inequalities for the Gaussian measure
S. Artstein-Avidan, M. Fradelizi, K. Wyczesany